Title

An Approximation Pricing Algorithm in an Incomplete Market: A Differential Geometric Approach

Publication Type

Journal Article

Publication Date

11-2004

Abstract

The minimal distance equivalent martingale measure (EMM) defined in Goll and Rⁿschendorf (2001) is the arbitrage-free equilibrium pricing measure. This paper provides an algorithm to approximate its density and the fair price of any contingent claim in an incomplete market. We first approximate the infinite dimensional space of all EMMs by a finite dimensional manifold of EMMs. A Riemannian geometric structure is shown on the manifold. An optimization algorithm on the Riemannian manifold becomes the approximation pricing algorithm. The financial interpretation of the geometry is also given in terms of pricing model risk.

Keywords

Incomplete markets, asset pricing, Riemannian manifold, cross entropy

Discipline

Finance and Financial Management | Portfolio and Security Analysis

Research Areas

Finance

Publication

Finance and Stochastics

Volume

8

Issue

4

First Page

501

Last Page

523

ISSN

0949-2984

Identifier

10.1007/s00780-004-0128-5

Publisher

Springer Verlag